Linear Equations with Ratios and Rates - Basic Arithmetic

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Question

I put in a bank account at a annual simple interest rate. How much interest will have accumulated after two years?

Answer

This is a simple interest rate problem, for which we use the formula:

Interest = P x r x t

P is the principal, or original loan amount; r is the annual interest rate; and t is the number of years in question.

In this problem, P = $9,000; r = 4%; and t = 2 years. Plugging these into the formula gives us:

$Interest=9,000\times \frac{4}{100}\times 2$

So, after two years the account has gathered $720 in interest.

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Question

If one recipe calls for eggs to make waffles, how many eggs are needed to make waffles?

Answer

To solve this problem, we can set up a proportion.

$\frac{\text{eggs}}{\text{waffles}}=\frac{\text{eggs}}{\text{waffles}}$

That proportion will tell us how many eggs go into each waffle. Since the number of eggs that goes into each waffle doesn't change, we can set these two proportions equal to each other.

Now, fill it in with the information we know:

$\frac{\text{6 eggs}}{\text{18 waffles}}=\frac{\text{x eggs}}{\text{30 waffles}}$

For the sake of making math easier, drop the words so we get the following equation:

$\frac{6}{18}=\frac{x}{30}$

To solve for x, cross-multiply this equation.

Divide both sides by 18.

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Question

The ratio of boys to girls in a class is . If there are boys in the class, how many girls are in the class?

Answer

We can write the following equation using the ratios given:

$\frac{3}{5}=\frac{12}{x}$

is the number of girls in the class.

Now, we can cross multiply to get the following equation:

Now divide both sides by .

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Question

If painters can paint houses in day, how many painters would it take to paint houses in day?

Answer

We can set up the following proportions using the given information:

$\frac{8\text{ painters}}{16\text{ houses}}=\frac{x\text{ painters}}{58\text{ houses}}$

Now, cross multiply these two fractions to get the following equation:

Divide both sides by .

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Question

If a car travels at miles per hour, how many hours would it take the car to travel miles?

Answer

We can write 40 miles per hour as the following fraction:

$\frac{40\text{ miles}}{1\text{ hour}}$

Since we want to figure out how many hours it takes a car to travel 200 miles, we can write the following equation:

$\frac{40\text{ miles}}{1\text{ hour}}=\frac{200\text{ miles}}{x\text{ hours}}$

Now, cross multiply.

Divide both sides by 40.

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Question

Jessica fills an aquarium with water. The aquarium can hold gallons of water—it's a huge aquarium! The faucet fills the tank at a rate of 1 gallon every 10 seconds. How long (in seconds) will it take Jessica to fill the tank?

Answer

The rate at which Jessica fills the tank can be written as a ratio:

$\frac{10 seconds}{1gallon}$

Multiply this ratio by the total amount of gallons possible to get the amount of time it takes to fill the tank.

$\frac{10seconds}{1gallon} \times 400 gallons = 4000 seconds$

Gallon units cancel out, so you are left with seconds as the final unit in the answer.

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